QCD Sum-Rule Calculation of the Kinetic Energy and Chromo-Interaction of Heavy Quarks Inside Mesons

Abstract

We present a QCD sum-rule determination of the heavy-quark kinetic energy inside a heavy meson, $-λ_1/2 m_Q$, which is consistent with the field-theory analog of the virial theorem. We obtain $-λ_1\approx (0.10\pm 0.05)~\mbox{GeV}^2$, significantly smaller than a previous sum-rule result, but in good agreement with recent determinations from the analysis of inclusive decays. We also present a new determination of the chromo-magnetic interaction, yielding $λ_2(m_b)=(0.15\pm 0.03)~\mbox{GeV}^2$. This implies $m_{B^*}^2-m_B^2=(0.60\pm 0.12)~\mbox{GeV}^2$, in good agreement with experiment. As a by-product of our analysis, we derive the QCD sum rules for the three form factors describing the meson matrix element of a velocity-changing current operator containing the gluon field-strength tensor.